The Bohr Radius Of

Remarks on the Bohr Phenomenon

Bohr’s theorem ([10]) states that analytic functions bounded by 1 in the unit disk have power series ∑ anz n such that ∑ |an||z| < 1 in the disk of radius 1/3 (the so-called Bohr radius.) On the other hand, it is known that there is no such Bohr phenomenon in Hardy spaces with the usual norm, although it is possible to build equivalent norms for which a Bohr phenomenon does occur! In this paper...

Generalization of Results about the Bohr Radius for Power Series

The Bohr radius for power series of holomorphic functions mapping Reinhardt domains D ⊂ C n into the convex domain G ⊂ C is independent of the domain G.

The Ecosphere and the Value of the Electromagnetic Fine Structure Constant

Following the coincidence A x atomic year ∼ Earth year (s), (A =Avogardo number, atomic year= aB/αc, aB = Bohr radius, α = fine structure constant, c = light velocity) and considering the ,,niche” for α, i. e. 180 ≤ α ≤ 85, the Ecosphere radius is calculated.

Generalization of Caratheodory’s Inequality and the Bohr Radius for Multidimensional Power Series

Bohr’s Power Series Theorem in Several Variables

Generalizing a classical one-variable theorem of Bohr, we show that if an n-variable power series has modulus less than 1 in the unit polydisc, then the sum of the moduli of the terms is less than 1 in the polydisc of radius 1/(3 √ n ). How large can the sum of the moduli of the terms of a convergent power series be? Harald Bohr addressed this question in 1914 with the following remarkable resu...